Regime Shifts in a Dynamic Term Structure Model of U.S. Treasury Bond Yields

This article develops and empirically implements an arbitrage-free,dynamic term structure model with "priced" factor and regime-shiftrisks. The risk factors are assumed to follow a discrete-timeGaussian process, and regime shifts are governed by a discrete-timeMarkov process with state-dependent transition probabilities.This model gives closed-form solutions for zero-coupon bondprices, an analytic representation of the likelihood functionfor bond yields, and a natural decomposition of expected excessreturns to components corresponding to regime-shift and factorrisks. Using monthly data on U.S. Treasury zero-coupon bondyields, we show a critical role of priced, state-dependent regime-shiftrisks in capturing the time variations in expected excess returns,and document notable differences in the behaviors of the factorrisk component of the expected returns across high and low volatilityregimes. Additionally, the state dependence of the regime-switchingprobabilities is shown to capture an interesting asymmetry inthe cyclical behavior of interest rates. The shapes of the termstructure of volatility of bond yield changes are also verydifferent across regimes, with the well-known hump being largelya low-volatility regime phenomenon.     

Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate

In this paper, we extend the one-factor, single regime shift, affine term structure model with time-dependent regime-shift probability to a multi-factor model. We model the nominal interest rate and the expected inflation rate, and estimate the term structure of the real interest rate in the Japanese government bond market using inflation-indexed bond data under zero interest rates. Incorporating the economic structure that the Bank of Japan terminates the zero interest rate when the expected inflation rate gets out of deflationary regime, we estimate the yield curve of the real interest rate for less than 10 years, consistent with the expectation of the market participants in the Japanese government bond market, where inflation-indexed bonds are traded for only around 10 years.     

Are regime-shift sources of risk priced in the market?

In this paper we develop a discrete-time pricing model for European options where the log-return of the underlying asset is subject to discontinuous regime shifts in its mean and/or volatility which follow a Markov chain. The model allows for multiple regime shifts whose risk cannot be hedge out and thus must be priced in option market. The paper provides estimates of the price of regime-shift risk coefficients based on a joint estimation procedure of the Markov regime-switching process of the underlying stock and the suggested option pricing model. The results of the paper indicate that bull-to-bear and bear-to-crash regime shifts carry substantial prices of risk. Risk averse investors in the markets price these regime shifts by assigning higher transition (switching) probabilities to them under the risk neutral probability measure than under the physical. Ignoring these sources of risk will lead to substantial option pricing errors. In addition, the paper shows that investors also price reverse regime shifts, like the crash-to-bear and bear-to-bull ones, by assigning smaller transition probabilities under the risk neutral measure than the physical. Finally, the paper evaluates the pricing performance of the model and indicates that it can be successfully employed, in practice, to price European options.     

An exact and explicit solution for the valuation of American put options

In this paper, an exact and explicit solution of the well-known Black–Scholes equation for the valuation of American put options is presented for the first time. To the best of the author's knowledge, a closed-form analytical formula has never been found for the valuation of American options of finite maturity, although there have been quite a few approximate solutions and numerical approaches proposed. The closed-form exact solution presented here is written in the form of a Taylor's series expansion, which contains infinitely many terms. However, only about 30 terms are actually needed to generate a convergent numerical solution if the solution of the corresponding European option is taken as the initial guess of the solution series. The optimal exercise boundary, which is the main difficulty of the problem, is found as an explicit function of the risk-free interest rate, the volatility and the time to expiration. A key feature of our solution procedure, which is based on the homotopy-analysis method, is the optimal exercise boundary being elegantly and temporarily removed in the solution process of each order, and, consequently, the solution of a linear problem can be analytically worked out at each order, resulting in a completely analytical and exact series-expansion solution for the optimal exercise boundary and the option price of American put options.     

Portfolio selection under the condition of value preservation

Besides risk and return, investors often are interested in choosing a portfolio such that the portfolio value is preserved. However, the traditional utility-maximizing approach generally fails to provide such a solution. As a different approach value preservation is formulated as an equilibrium problem. Following this approach it is shown that under reasonable assumptions a value preserving solution exists. The solution only depends on the set of feasable portfolio decisions. Contrary to this, the Bernoulli principle in addition requires a utility function that is independent from this set.     

Robust utility maximization for a diffusion market model with misspecified coefficients

The paper studies the robust maximization of utility from terminal wealth in a diffusion financial market model. The underlying model consists of a tradable risky asset whose price is described by a diffusion process with misspecified trend and volatility coefficients, and a non-tradable asset with a known parameter. The robust functional is defined in terms of a utility function. An explicit characterization of the solution is given via the solution of the Hamilton–Jacobi–Bellman–Isaacs (HJBI) equation.     

Evolution of a Lease Solution

The lease solution most frequently advocated in the literature, that in which the after-tax cash flows of leasing and borrowing are discounted by the after-tax borrowing rate, is invariably associated with Myers, Dill and Bautista (MDB; 1976). This article, while accepting the basic assumptions underlying this solution, attempts to identify its origin and the process by which it evolved. The finding is that Bierman and Smidt (1966) pioneered this approach which has its antecedents in the works of Gant (1959) and McEachron (1959). Post-MDB developments in this solution are analysed and a critique is offered of an alternative evaluation approach advocated in MDB's influential work.     

Valuation of Portfolio Credit Derivatives with Default Intensities Using the Vasicek Model

We present a methodology for valuing portfolio credit derivatives under a reduced form model for which the default intensity processes of risk assets follow the one-factor Vasicek model. A closed-form solution of joint survival time distribution is obtained. The solution is applied to value credit derivatives of a credit default swap index and collateralized debt obligation. The limitation of methods using the Vasicek model is discussed. We propose that the method is valid and efficient for a portfolio with small-scale correlated risk assets, for which the acceptable size is much greater than for the traditional method. Numerical examples and parameter analysis are also presented.     

An approximation algorithm for optimal consumption/investment problems

This article develops a simple approach to solving continuous-time portfolio choice problems. Portfolio problems for which no closed-form solutions are available may be handled by this technique, which substitutes the numerical solution of partial differential equations with a non-linear numerical algorithm approximating the solution. This paper complements the wide literature in economics on the solution of dynamic problems in discrete time using projection methods. Our approach extends the approximation function to power forms, which are shown to fit finance type problems well. The algorithm is parsimonious, and is first illustrated by solving two basic examples, first, the standard Merton problem, and second, a jump-diffusion problem. Then, we demonstrate that the model is easy to implement on a larger scale, by optimizing a portfolio of six stock indexes, and stochastic volatility driven by two correlated state variables. Copyright © 2002 John Wiley & Sons, Ltd.     

Pricing Perpetual Put Options by the Black–Scholes Equation with a Nonlinear Volatility Function

We investigate qualitative and quantitative behavior of a solution of the mathematical model for pricing American style of perpetual put options. We assume the option price is a solution to the stationary generalized Black–Scholes equation in which the volatility function may depend on the second derivative of the option price itself. We prove existence and uniqueness of a solution to the free boundary problem. We derive a single implicit equation for the free boundary position and the closed form formula for the option price. It is a generalization of the well-known explicit closed form solution derived by Merton for the case of a constant volatility. We also present results of numerical computations of the free boundary position, option price and their dependence on model parameters.     

A closed-form solution for options with stochastic volatility with applications to bond and currency options

I use a new technique to derive a closed-form solution for theprice of a European call option on an asset with stochasticvolatility. The model allows arbitrary correlation between volatilityand spot asset returns. I introduce stochastic interest ratesand show how to apply the model to bond options and foreigncurrency options. Simulations show that correlation betweenvolatility and the spot asset's price is important for explainingreturn skewness and strike-price biases in the Black-Scholes(1973) model. The solution technique is based on characteristicfunctions and can be applied to other problems     

我国保险消费纠纷的替代性解决机制分析

目前我国的保险消费纠纷替代性解决机制看似多元,实则并没有为保险消费者提供一个多元、畅通和低成本的救济渠道,因此亟待从维护保险消费者权益和便利消费者维权的角度出发,构建一公平、合理与便捷的保险消费纠纷替代性解决机制。从根本上讲,要本着保护消费者的目的,对我国保险消费纠纷替代性解决机制做出体系化、专业化和结构化的思考,从而...     

The solution to the forward-bias puzzle: Reply

My proposed econometric solution to the forward-bias puzzle provoked several comments. Those comments raise three primary objections to my solution. (1) It suffers from multicollinearity, miss-specification and other serious econometric problems. (2) My key test equation is a tautology or identity. (3) My econometric solution has nothing to do with either the forward-bias puzzle or uncovered interest parity. This is my reply to those objections.     

An analysis of a three-factor model proposed by the Danish Society of Actuaries for forecasting and risk analysis

This paper provides the explicit solution to the three-factor diffusion model recently proposed by the Danish Society of Actuaries to the Danish industry of life insurance and pensions. The solution is obtained by use of the known general solution to multidimensional linear stochastic differential equation systems. With offset in the explicit solution, we establish the conditional distribution of the future state variables which allows for exact simulation. Using exact simulation, we illustrate how simulation of the system can be improved compared to a standard Euler scheme. In order to analyze the effect of choosing the exact simulation scheme over the traditional Euler approximation scheme frequently applied by practitioners, we carry out a simulation study. We show that due to its recursive nature, the Euler scheme becomes computationally expensive as it requires a small step size in order to minimize discretization errors. Using our exact simulation scheme, one is able to cut these computational costs significantly and obtain even better forecasts. As probability density tail behavior is key to expected investment portfolio performance, we further conduct a risk analysis in which we compare well-known risk measures under both schemes. Finally, we conduct a sensitivity analysis and find that the relative performance of the two schemes depends on the chosen model parameter estimates.     

Asset prices,asset stocks and rational expectations

This paper explores the relationship between asset return covariances and the impact of asset stock changes on asset prices. In the process the paper reconciles recent contradictory results on the effect of changes in the stock of government debt on equity prices. A solution for asset prices in a rational expectations equilibrium is also derived. This solution has the property that at the prices implied by the solution the demand for each asset equals its supply and the distribution of future asset prices implied by the solution is identical to the distribution upon which asset holders base their demands.     

Entrepreneurial Financing and Costly Due Diligence

In the traditional solution to the adverse selection problem, entrepreneurs indirectly signal quality via security choice, typically debt. This paper models an alternative solution. The costly due diligence of venture capitalists directly reveals the quality of projects, thereby reducing information asymmetry. It is shown that this mechanism necessitates profit-sharing, a contractual feature usually associated in the literature with managerial agency costs rather than adverse selection.     

Stochastic reserve changes and expansion of bank credit: The case of additional risks

In this paper we examine the effects of introducing additional risks to the Orr-Mellon-Cooper model on the asymptotic behavior of bank credit expansion, and derive monetary policy implications therefrom. Our model of additional risks corrects a loss of generality existing in the Orr-Mellon-Cooper model. It shows that the local solution for optimal credit expansion is the global solution, regardless of the parameters of the reserve loss functions, when the default risk is introduced. The analysis further points out necessary conditions to determine the direction of credit changes caused by a monetary injection under uncertainty.     

Exponential utility maximization under partial information

We consider the exponential utility maximization problem under partial information. The underlying asset price process follows a continuous semimartingale and strategies have to be constructed when only part of the information in the market is available. We show that this problem is equivalent to a new exponential optimization problem which is formulated in terms of observable processes. We prove that the value process of the reduced problem is the unique solution of a backward stochastic differential equation (BSDE) which characterizes the optimal strategy. We examine two particular cases of diffusion market models for which an explicit solution has been provided. Finally, we study the issue of sufficiency of partial information.